Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.43449.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1400) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.04673\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.04673 | 1.18168 | 0.590840 | − | 0.806789i | \(-0.298797\pi\) | ||||
0.590840 | + | 0.806789i | \(0.298797\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.18910 | 0.396367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.56405 | −1.07460 | −0.537301 | − | 0.843391i | \(-0.680556\pi\) | ||||
−0.537301 | + | 0.843391i | \(0.680556\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.90761 | 0.806426 | 0.403213 | − | 0.915106i | \(-0.367893\pi\) | ||||
0.403213 | + | 0.915106i | \(0.367893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.71851 | 0.901871 | 0.450935 | − | 0.892557i | \(-0.351090\pi\) | ||||
0.450935 | + | 0.892557i | \(0.351090\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.57939 | −0.821168 | −0.410584 | − | 0.911823i | \(-0.634675\pi\) | ||||
−0.410584 | + | 0.911823i | \(0.634675\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.10880 | −0.648229 | −0.324114 | − | 0.946018i | \(-0.605066\pi\) | ||||
−0.324114 | + | 0.946018i | \(0.605066\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.70642 | −0.713301 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.57939 | 0.293285 | 0.146642 | − | 0.989190i | \(-0.453153\pi\) | ||||
0.146642 | + | 0.989190i | \(0.453153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.764171 | −0.137249 | −0.0686245 | − | 0.997643i | \(-0.521861\pi\) | ||||
−0.0686245 | + | 0.997643i | \(0.521861\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.29465 | −1.26983 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00107 | −1.15097 | −0.575484 | − | 0.817813i | \(-0.695186\pi\) | ||||
−0.575484 | + | 0.817813i | \(0.695186\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.95109 | 0.952937 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.07812 | 1.10542 | 0.552708 | − | 0.833375i | \(-0.313594\pi\) | ||||
0.552708 | + | 0.833375i | \(0.313594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9390 | −1.66818 | −0.834091 | − | 0.551627i | \(-0.814007\pi\) | ||||
−0.834091 | + | 0.551627i | \(0.814007\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.37602 | −1.07590 | −0.537951 | − | 0.842976i | \(-0.680802\pi\) | ||||
−0.537951 | + | 0.842976i | \(0.680802\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.61078 | 1.06572 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.32822 | 0.457166 | 0.228583 | − | 0.973524i | \(-0.426591\pi\) | ||||
0.228583 | + | 0.973524i | \(0.426591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.32604 | −0.970357 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.14019 | 1.05976 | 0.529881 | − | 0.848072i | \(-0.322237\pi\) | ||||
0.529881 | + | 0.848072i | \(0.322237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.93793 | −0.760274 | −0.380137 | − | 0.924930i | \(-0.624123\pi\) | ||||
−0.380137 | + | 0.924930i | \(0.624123\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0021 | −1.71063 | −0.855316 | − | 0.518106i | \(-0.826637\pi\) | ||||
−0.855316 | + | 0.518106i | \(0.826637\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.36286 | −0.765999 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.5305 | −1.72445 | −0.862225 | − | 0.506525i | \(-0.830930\pi\) | ||||
−0.862225 | + | 0.506525i | \(0.830930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.2216 | 1.54747 | 0.773733 | − | 0.633512i | \(-0.218387\pi\) | ||||
0.773733 | + | 0.633512i | \(0.218387\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.98466 | 0.335801 | 0.167900 | − | 0.985804i | \(-0.446301\pi\) | ||||
0.167900 | + | 0.985804i | \(0.446301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1533 | −1.23926 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8923 | −1.19558 | −0.597791 | − | 0.801652i | \(-0.703955\pi\) | ||||
−0.597791 | + | 0.801652i | \(0.703955\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.23258 | 0.346569 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.71958 | 0.500274 | 0.250137 | − | 0.968210i | \(-0.419524\pi\) | ||||
0.250137 | + | 0.968210i | \(0.419524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.56405 | −0.162184 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6575 | 1.08211 | 0.541053 | − | 0.840988i | \(-0.318026\pi\) | ||||
0.541053 | + | 0.840988i | \(0.318026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.23801 | −0.425936 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.15552 | −0.811505 | −0.405753 | − | 0.913983i | \(-0.632991\pi\) | ||||
−0.405753 | + | 0.913983i | \(0.632991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.34463 | −0.920753 | −0.460377 | − | 0.887724i | \(-0.652286\pi\) | ||||
−0.460377 | + | 0.887724i | \(0.652286\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.81090 | −0.561761 | −0.280880 | − | 0.959743i | \(-0.590626\pi\) | ||||
−0.280880 | + | 0.959743i | \(0.590626\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.7163 | 1.40957 | 0.704784 | − | 0.709422i | \(-0.251044\pi\) | ||||
0.704784 | + | 0.709422i | \(0.251044\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.3293 | −1.36008 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0164044 | 0.00154319 | 0.000771596 | − | 1.00000i | \(-0.499754\pi\) | ||||
0.000771596 | 1.00000i | \(0.499754\pi\) | ||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.45744 | 0.319640 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.70245 | 0.154769 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.4870 | 1.30625 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9044 | 1.41128 | 0.705642 | − | 0.708569i | \(-0.250659\pi\) | ||||
0.705642 | + | 0.708569i | \(0.250659\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.3892 | −1.97126 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.2490 | −1.59442 | −0.797211 | − | 0.603701i | \(-0.793692\pi\) | ||||
−0.797211 | + | 0.603701i | \(0.793692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.69992 | −0.743284 | −0.371642 | − | 0.928376i | \(-0.621205\pi\) | ||||
−0.371642 | + | 0.928376i | \(0.621205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3728 | −0.964625 | −0.482313 | − | 0.875999i | \(-0.660203\pi\) | ||||
−0.482313 | + | 0.875999i | \(0.660203\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.0967 | −1.27137 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.3629 | −0.866586 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.8009 | −1.37639 | −0.688194 | − | 0.725527i | \(-0.741596\pi\) | ||||
−0.688194 | + | 0.725527i | \(0.741596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.48593 | 0.609196 | 0.304598 | − | 0.952481i | \(-0.401478\pi\) | ||||
0.304598 | + | 0.952481i | \(0.401478\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.42168 | 0.357472 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.7032 | 1.17344 | 0.586720 | − | 0.809790i | \(-0.300419\pi\) | ||||
0.586720 | + | 0.809790i | \(0.300419\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.81197 | 0.540224 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.39354 | 0.500781 | 0.250390 | − | 0.968145i | \(-0.419441\pi\) | ||||
0.250390 | + | 0.968145i | \(0.419441\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8509 | 1.22658 | 0.613291 | − | 0.789857i | \(-0.289845\pi\) | ||||
0.613291 | + | 0.789857i | \(0.289845\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.54581 | −0.349678 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.25625 | −0.325484 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.25082 | −0.551269 | −0.275635 | − | 0.961262i | \(-0.588888\pi\) | ||||
−0.275635 | + | 0.961262i | \(0.588888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.6608 | 1.25230 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5998 | 1.01649 | 0.508247 | − | 0.861211i | \(-0.330294\pi\) | ||||
0.508247 | + | 0.861211i | \(0.330294\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5469 | 1.22992 | 0.614960 | − | 0.788558i | \(-0.289172\pi\) | ||||
0.614960 | + | 0.788558i | \(0.289172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.1533 | −0.898401 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.2530 | −0.969152 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.63043 | −0.624476 | −0.312238 | − | 0.950004i | \(-0.601079\pi\) | ||||
−0.312238 | + | 0.950004i | \(0.601079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.6739 | −0.984270 | −0.492135 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492135 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.8922 | −1.91599 | −0.957996 | − | 0.286783i | \(-0.907414\pi\) | ||||
−0.957996 | + | 0.286783i | \(0.907414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.68493 | 0.261218 | 0.130609 | − | 0.991434i | \(-0.458307\pi\) | ||||
0.130609 | + | 0.991434i | \(0.458307\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.6586 | −2.02142 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.69667 | −0.256936 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.7571 | 0.882428 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.91193 | 0.338151 | 0.169075 | − | 0.985603i | \(-0.445922\pi\) | ||||
0.169075 | + | 0.985603i | \(0.445922\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −29.7399 | −2.03775 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 27.0609 | 1.82861 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.8120 | 0.727292 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6575 | 0.847609 | 0.423805 | − | 0.905754i | \(-0.360694\pi\) | ||||
0.423805 | + | 0.905754i | \(0.360694\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.94007 | 0.527001 | 0.263500 | − | 0.964659i | \(-0.415123\pi\) | ||||
0.263500 | + | 0.964659i | \(0.415123\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.64039 | −0.438809 | −0.219405 | − | 0.975634i | \(-0.570411\pi\) | ||||
−0.219405 | + | 0.975634i | \(0.570411\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.7042 | 0.897794 | 0.448897 | − | 0.893583i | \(-0.351817\pi\) | ||||
0.448897 | + | 0.893583i | \(0.351817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.10880 | 0.396809 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.0010 | 1.81124 | 0.905618 | − | 0.424095i | \(-0.139408\pi\) | ||||
0.905618 | + | 0.424095i | \(0.139408\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.8477 | −1.47175 | −0.735874 | − | 0.677118i | \(-0.763228\pi\) | ||||
−0.735874 | + | 0.677118i | \(0.763228\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.7086 | −0.751107 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.4075 | −0.662211 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.2935 | −1.41279 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.55973 | −0.224688 | −0.112344 | − | 0.993669i | \(-0.535836\pi\) | ||||
−0.112344 | + | 0.993669i | \(0.535836\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.0799 | 0.696588 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.6239 | 1.72313 | 0.861567 | − | 0.507644i | \(-0.169484\pi\) | ||||
0.861567 | + | 0.507644i | \(0.169484\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.87805 | 0.116248 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.2226 | −1.55529 | −0.777647 | − | 0.628701i | \(-0.783587\pi\) | ||||
−0.777647 | + | 0.628701i | \(0.783587\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.65969 | 0.591164 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.6389 | −1.01449 | −0.507246 | − | 0.861801i | \(-0.669337\pi\) | ||||
−0.507246 | + | 0.861801i | \(0.669337\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.5262 | −1.48986 | −0.744929 | − | 0.667144i | \(-0.767517\pi\) | ||||
−0.744929 | + | 0.667144i | \(0.767517\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.5793 | −1.89742 | −0.948709 | − | 0.316150i | \(-0.897610\pi\) | ||||
−0.948709 | + | 0.316150i | \(0.897610\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.908675 | −0.0544010 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.0413 | −1.67280 | −0.836402 | − | 0.548117i | \(-0.815345\pi\) | ||||
−0.836402 | + | 0.548117i | \(0.815345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.6707 | −1.76374 | −0.881869 | − | 0.471495i | \(-0.843715\pi\) | ||||
−0.881869 | + | 0.471495i | \(0.843715\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.17270 | −0.186629 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.8130 | 1.27870 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.43031 | −0.550925 | −0.275462 | − | 0.961312i | \(-0.588831\pi\) | ||||
−0.275462 | + | 0.961312i | \(0.588831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.2099 | 0.766515 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.03916 | −0.522748 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.6922 | −0.958939 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.59798 | −0.262420 | −0.131210 | − | 0.991355i | \(-0.541886\pi\) | ||||
−0.131210 | + | 0.991355i | \(0.541886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.1259 | −1.08804 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.48055 | −0.0839540 | −0.0419770 | − | 0.999119i | \(-0.513366\pi\) | ||||
−0.0419770 | + | 0.999119i | \(0.513366\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.1402 | −0.968821 | −0.484410 | − | 0.874841i | \(-0.660966\pi\) | ||||
−0.484410 | + | 0.874841i | \(0.660966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.86301 | −0.385465 | −0.192733 | − | 0.981251i | \(-0.561735\pi\) | ||||
−0.192733 | + | 0.981251i | \(0.561735\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.62902 | −0.315164 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.8933 | −0.663821 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.3100 | −0.740587 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 30.1203 | 1.66566 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.41736 | −0.187835 | −0.0939176 | − | 0.995580i | \(-0.529939\pi\) | ||||
−0.0939176 | + | 0.995580i | \(0.529939\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.32497 | −0.456206 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.3574 | 1.43578 | 0.717890 | − | 0.696156i | \(-0.245108\pi\) | ||||
0.717890 | + | 0.696156i | \(0.245108\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.0335753 | 0.00182356 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.72354 | 0.147488 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.54653 | 0.512485 | 0.256242 | − | 0.966613i | \(-0.417516\pi\) | ||||
0.256242 | + | 0.966613i | \(0.417516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.8259 | −0.579496 | −0.289748 | − | 0.957103i | \(-0.593572\pi\) | ||||
−0.289748 | + | 0.957103i | \(0.593572\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.7768 | −0.575224 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.6443 | 1.09879 | 0.549393 | − | 0.835564i | \(-0.314859\pi\) | ||||
0.549393 | + | 0.835564i | \(0.314859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.6860 | 1.14454 | 0.572272 | − | 0.820064i | \(-0.306062\pi\) | ||||
0.572272 | + | 0.820064i | \(0.306062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.18798 | −0.325683 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.48446 | 0.182887 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.8120 | −0.981977 | −0.490988 | − | 0.871166i | \(-0.663364\pi\) | ||||
−0.490988 | + | 0.871166i | \(0.663364\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.41660 | 0.438150 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.1818 | 1.45920 | 0.729600 | − | 0.683874i | \(-0.239706\pi\) | ||||
0.729600 | + | 0.683874i | \(0.239706\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.59224 | 0.236512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.93397 | −0.356174 | −0.178087 | − | 0.984015i | \(-0.556991\pi\) | ||||
−0.178087 | + | 0.984015i | \(0.556991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.5519 | 1.66769 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.1488 | 0.774069 | 0.387034 | − | 0.922065i | \(-0.373499\pi\) | ||||
0.387034 | + | 0.922065i | \(0.373499\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.0076 | −0.661212 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.1606 | 1.32639 | 0.663196 | − | 0.748445i | \(-0.269199\pi\) | ||||
0.663196 | + | 0.748445i | \(0.269199\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5601 | −0.584619 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −37.3507 | −1.88409 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.0561 | −1.00659 | −0.503293 | − | 0.864116i | \(-0.667878\pi\) | ||||
−0.503293 | + | 0.864116i | \(0.667878\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.4509 | 0.571833 | 0.285916 | − | 0.958255i | \(-0.407702\pi\) | ||||
0.285916 | + | 0.958255i | \(0.407702\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.22191 | −0.110681 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.9522 | 1.23683 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.6218 | −1.31636 | −0.658182 | − | 0.752859i | \(-0.728674\pi\) | ||||
−0.658182 | + | 0.752859i | \(0.728674\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.8064 | −0.878324 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.2770 | −1.13988 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.8944 | 1.31388 | 0.656939 | − | 0.753944i | \(-0.271851\pi\) | ||||
0.656939 | + | 0.753944i | \(0.271851\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.2662 | −0.938975 | −0.469487 | − | 0.882939i | \(-0.655561\pi\) | ||||
−0.469487 | + | 0.882939i | \(0.655561\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.77082 | −0.426452 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.2100 | −1.02403 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.2355 | 0.974709 | 0.487354 | − | 0.873204i | \(-0.337962\pi\) | ||||
0.487354 | + | 0.873204i | \(0.337962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.13135 | 0.150483 | 0.0752416 | − | 0.997165i | \(-0.476027\pi\) | ||||
0.0752416 | + | 0.997165i | \(0.476027\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.1276 | 0.532305 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.4585 | −0.833247 | −0.416623 | − | 0.909079i | \(-0.636787\pi\) | ||||
−0.416623 | + | 0.909079i | \(0.636787\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5619 | 0.644344 | 0.322172 | − | 0.946681i | \(-0.395587\pi\) | ||||
0.322172 | + | 0.946681i | \(0.395587\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.3870 | −1.62645 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.7260 | −1.35566 | −0.677832 | − | 0.735216i | \(-0.737081\pi\) | ||||
−0.677832 | + | 0.735216i | \(0.737081\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.2268 | −1.18788 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.3217 | 0.719875 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.23873 | −0.385392 | −0.192696 | − | 0.981259i | \(-0.561723\pi\) | ||||
−0.192696 | + | 0.981259i | \(0.561723\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.7824 | −0.643305 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.8729 | −1.39132 | −0.695660 | − | 0.718371i | \(-0.744888\pi\) | ||||
−0.695660 | + | 0.718371i | \(0.744888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4155 | 0.530525 | 0.265262 | − | 0.964176i | \(-0.414541\pi\) | ||||
0.265262 | + | 0.964176i | \(0.414541\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.2223 | 1.16715 | 0.583574 | − | 0.812060i | \(-0.301654\pi\) | ||||
0.583574 | + | 0.812060i | \(0.301654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.0934 | 1.38663 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 38.9871 | 1.79263 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.95759 | 0.181206 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.0788 | 1.23726 | 0.618632 | − | 0.785681i | \(-0.287687\pi\) | ||||
0.618632 | + | 0.785681i | \(0.287687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.3564 | −0.928170 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3464 | 0.831355 | 0.415678 | − | 0.909512i | \(-0.363544\pi\) | ||||
0.415678 | + | 0.909512i | \(0.363544\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.0858 | 0.591762 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.4457 | −1.14835 | −0.574173 | − | 0.818734i | \(-0.694676\pi\) | ||||
−0.574173 | + | 0.818734i | \(0.694676\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.87297 | 0.264505 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.14309 | 0.185470 | 0.0927350 | − | 0.995691i | \(-0.470439\pi\) | ||||
0.0927350 | + | 0.995691i | \(0.470439\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.4426 | 1.44943 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.0099 | −0.847610 | −0.423805 | − | 0.905754i | \(-0.639306\pi\) | ||||
−0.423805 | + | 0.905754i | \(0.639306\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.30405 | −0.413207 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.84589 | −0.170466 | −0.0852331 | − | 0.996361i | \(-0.527163\pi\) | ||||
−0.0852331 | + | 0.996361i | \(0.527163\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.2667 | 0.585740 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.2885 | 1.15617 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.8405 | −0.651424 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.6154 | 0.596504 | 0.298252 | − | 0.954487i | \(-0.403596\pi\) | ||||
0.298252 | + | 0.954487i | \(0.403596\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.1673 | −0.969307 | −0.484653 | − | 0.874706i | \(-0.661054\pi\) | ||||
−0.484653 | + | 0.874706i | \(0.661054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.84157 | −0.123781 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.3354 | −0.579800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.67950 | 0.420054 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.5804 | 0.891436 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.8350 | 1.20117 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0149 | 1.24745 | 0.623725 | − | 0.781644i | \(-0.285619\pi\) | ||||
0.623725 | + | 0.781644i | \(0.285619\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.8670 | 1.45337 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.6053 | 1.22308 | 0.611538 | − | 0.791215i | \(-0.290551\pi\) | ||||
0.611538 | + | 0.791215i | \(0.290551\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.06080 | −0.301348 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.65324 | −0.240836 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.6304 | 1.34022 | 0.670111 | − | 0.742261i | \(-0.266246\pi\) | ||||
0.670111 | + | 0.742261i | \(0.266246\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.8063 | −1.34526 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.1252 | −1.14523 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.0110 | −0.843364 | −0.421682 | − | 0.906744i | \(-0.638560\pi\) | ||||
−0.421682 | + | 0.906744i | \(0.638560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.3446 | 1.48172 | 0.740861 | − | 0.671659i | \(-0.234418\pi\) | ||||
0.740861 | + | 0.671659i | \(0.234418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.6707 | −0.655797 | −0.327898 | − | 0.944713i | \(-0.606340\pi\) | ||||
−0.327898 | + | 0.944713i | \(0.606340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.6642 | −0.737931 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.9057 | −1.07847 | −0.539235 | − | 0.842156i | \(-0.681286\pi\) | ||||
−0.539235 | + | 0.842156i | \(0.681286\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.9868 | −1.16309 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.8619 | −0.491272 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.2409 | −1.57837 | −0.789185 | − | 0.614156i | \(-0.789497\pi\) | ||||
−0.789185 | + | 0.614156i | \(0.789497\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.73526 | 0.112705 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −55.0411 | −2.26409 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −46.2697 | −1.90007 | −0.950034 | − | 0.312148i | \(-0.898952\pi\) | ||||
−0.950034 | + | 0.312148i | \(0.898952\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.54206 | 0.308676 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.0525 | −0.860180 | −0.430090 | − | 0.902786i | \(-0.641518\pi\) | ||||
−0.430090 | + | 0.902786i | \(0.641518\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.5283 | 1.12290 | 0.561451 | − | 0.827510i | \(-0.310243\pi\) | ||||
0.561451 | + | 0.827510i | \(0.310243\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.6499 | −0.678038 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.6514 | 0.878802 | 0.439401 | − | 0.898291i | \(-0.355191\pi\) | ||||
0.439401 | + | 0.898291i | \(0.355191\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.4466 | −0.867635 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.2336 | 1.05956 | 0.529782 | − | 0.848134i | \(-0.322274\pi\) | ||||
0.529782 | + | 0.848134i | \(0.322274\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.48553 | 0.381873 | 0.190937 | − | 0.981602i | \(-0.438848\pi\) | ||||
0.190937 | + | 0.981602i | \(0.438848\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.13942 | 0.246764 | 0.123382 | − | 0.992359i | \(-0.460626\pi\) | ||||
0.123382 | + | 0.992359i | \(0.460626\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.5225 | 0.462382 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26.1104 | 1.04275 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.0335 | −1.03802 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.8070 | 1.46527 | 0.732633 | − | 0.680624i | \(-0.238291\pi\) | ||||
0.732633 | + | 0.680624i | \(0.238291\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.0534 | 0.399586 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.2782 | −0.683515 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.6440 | −0.775892 | −0.387946 | − | 0.921682i | \(-0.626815\pi\) | ||||
−0.387946 | + | 0.921682i | \(0.626815\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.8590 | 0.704292 | 0.352146 | − | 0.935945i | \(-0.385452\pi\) | ||||
0.352146 | + | 0.935945i | \(0.385452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.4303 | 0.921141 | 0.460570 | − | 0.887623i | \(-0.347645\pi\) | ||||
0.460570 | + | 0.887623i | \(0.347645\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.0120 | −1.13882 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.04348 | 0.119101 | 0.0595503 | − | 0.998225i | \(-0.481033\pi\) | ||||
0.0595503 | + | 0.998225i | \(0.481033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.7218 | 0.613364 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.576904 | −0.0224730 | −0.0112365 | − | 0.999937i | \(-0.503577\pi\) | ||||
−0.0112365 | + | 0.999937i | \(0.503577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.1584 | −1.09523 | −0.547617 | − | 0.836729i | \(-0.684465\pi\) | ||||
−0.547617 | + | 0.836729i | \(0.684465\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.1292 | 0.859426 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.90999 | −0.190116 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.9065 | 1.00160 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1631 | 0.816992 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.7835 | −0.685503 | −0.342751 | − | 0.939426i | \(-0.611359\pi\) | ||||
−0.342751 | + | 0.939426i | \(0.611359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.6768 | 1.25587 | 0.627936 | − | 0.778265i | \(-0.283900\pi\) | ||||
0.627936 | + | 0.778265i | \(0.283900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.2512 | 0.622746 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.1351 | 0.617393 | 0.308696 | − | 0.951161i | \(-0.400107\pi\) | ||||
0.308696 | + | 0.951161i | \(0.400107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.5911 | −0.518532 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.67716 | 0.368671 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.1862 | 0.615750 | 0.307875 | − | 0.951427i | \(-0.400382\pi\) | ||||
0.307875 | + | 0.951427i | \(0.400382\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.3201 | 0.996943 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.0489 | 1.06091 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.8684 | 0.750419 | 0.375210 | − | 0.926940i | \(-0.377571\pi\) | ||||
0.375210 | + | 0.926940i | \(0.377571\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.0595 | 0.945138 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.7667 | −0.930131 | −0.465066 | − | 0.885276i | \(-0.653969\pi\) | ||||
−0.465066 | + | 0.885276i | \(0.653969\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.54906 | 0.133100 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.37565 | 0.0889688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 57.3105 | 2.14030 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.44692 | −0.277723 | −0.138862 | − | 0.990312i | \(-0.544344\pi\) | ||||
−0.138862 | + | 0.990312i | \(0.544344\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.7630 | −1.73913 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.63572 | −0.0977534 | −0.0488767 | − | 0.998805i | \(-0.515564\pi\) | ||||
−0.0488767 | + | 0.998805i | \(0.515564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.49568 | 0.351692 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.6768 | −1.50448 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.3811 | 0.457305 | 0.228652 | − | 0.973508i | \(-0.426568\pi\) | ||||
0.228652 | + | 0.973508i | \(0.426568\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 49.9043 | 1.83825 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.73025 | 0.247576 | 0.123788 | − | 0.992309i | \(-0.460496\pi\) | ||||
0.123788 | + | 0.992309i | \(0.460496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.3012 | −0.782521 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.6268 | 0.683352 | 0.341676 | − | 0.939818i | \(-0.389005\pi\) | ||||
0.341676 | + | 0.939818i | \(0.389005\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.9520 | −0.473889 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.4245 | −1.51160 | −0.755801 | − | 0.654801i | \(-0.772752\pi\) | ||||
−0.755801 | + | 0.654801i | \(0.772752\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.28581 | −0.265510 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.3296 | 0.993311 | 0.496655 | − | 0.867948i | \(-0.334561\pi\) | ||||
0.496655 | + | 0.867948i | \(0.334561\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.6776 | 0.823143 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5651 | 0.491735 | 0.245868 | − | 0.969303i | \(-0.420927\pi\) | ||||
0.245868 | + | 0.969303i | \(0.420927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.6685 | 0.854619 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.6618 | −1.21388 | −0.606938 | − | 0.794749i | \(-0.707602\pi\) | ||||
−0.606938 | + | 0.794749i | \(0.707602\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.5387 | 2.03619 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.06100 | 0.0381615 | 0.0190808 | − | 0.999818i | \(-0.493926\pi\) | ||||
0.0190808 | + | 0.999818i | \(0.493926\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.3353 | −0.907733 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.7873 | 1.85310 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.85388 | −0.209200 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.3760 | −1.43925 | −0.719625 | − | 0.694363i | \(-0.755686\pi\) | ||||
−0.719625 | + | 0.694363i | \(0.755686\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −51.6239 | −1.83786 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.2652 | −0.613105 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.16436 | −0.218353 | −0.109176 | − | 0.994022i | \(-0.534821\pi\) | ||||
−0.109176 | + | 0.994022i | \(0.534821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.4278 | −0.970325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.61205 | 0.198292 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −47.1223 | −1.66291 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.0554 | −1.19881 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.0767 | −0.987123 | −0.493561 | − | 0.869711i | \(-0.664305\pi\) | ||||
−0.493561 | + | 0.869711i | \(0.664305\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.3175 | −1.41574 | −0.707869 | − | 0.706343i | \(-0.750344\pi\) | ||||
−0.707869 | + | 0.706343i | \(0.750344\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −50.1984 | −1.76053 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39.1549 | 1.36986 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.6600 | 1.90765 | 0.953823 | − | 0.300368i | \(-0.0971094\pi\) | ||||
0.953823 | + | 0.300368i | \(0.0971094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.0682 | 0.873821 | 0.436911 | − | 0.899505i | \(-0.356073\pi\) | ||||
0.436911 | + | 0.899505i | \(0.356073\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.8101 | 0.688866 | 0.344433 | − | 0.938811i | \(-0.388071\pi\) | ||||
0.344433 | + | 0.938811i | \(0.388071\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.2693 | 0.703982 | 0.351991 | − | 0.936003i | \(-0.385505\pi\) | ||||
0.351991 | + | 0.936003i | \(0.385505\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −64.6344 | −2.24214 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.83234 | 0.0978999 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.3873 | 1.87766 | 0.938829 | − | 0.344384i | \(-0.111912\pi\) | ||||
0.938829 | + | 0.344384i | \(0.111912\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.5055 | −0.913984 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −57.3929 | −1.97672 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −60.7278 | −2.08417 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.7649 | 0.746091 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.88160 | −0.132903 | −0.0664517 | − | 0.997790i | \(-0.521168\pi\) | ||||
−0.0664517 | + | 0.997790i | \(0.521168\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.1826 | 0.962699 | 0.481350 | − | 0.876529i | \(-0.340147\pi\) | ||||
0.481350 | + | 0.876529i | \(0.340147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5009 | 0.631241 | 0.315621 | − | 0.948885i | \(-0.397787\pi\) | ||||
0.315621 | + | 0.948885i | \(0.397787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.0653 | 0.478787 | 0.239394 | − | 0.970923i | \(-0.423051\pi\) | ||||
0.239394 | + | 0.970923i | \(0.423051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.49365 | −0.220536 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.6375 | −0.360852 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.7127 | −1.37950 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.6728 | 0.428911 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.5677 | 0.458147 | 0.229074 | − | 0.973409i | \(-0.426430\pi\) | ||||
0.229074 | + | 0.973409i | \(0.426430\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.3013 | −0.651017 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.90324 | 0.333649 | 0.166824 | − | 0.985987i | \(-0.446649\pi\) | ||||
0.166824 | + | 0.985987i | \(0.446649\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.4705 | 0.924456 | 0.462228 | − | 0.886761i | \(-0.347050\pi\) | ||||
0.462228 | + | 0.886761i | \(0.347050\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.8458 | −1.20359 | −0.601793 | − | 0.798652i | \(-0.705547\pi\) | ||||
−0.601793 | + | 0.798652i | \(0.705547\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 39.7511 | 1.33171 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.4016 | 0.883497 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.5007 | −0.617721 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.20692 | −0.0402531 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.3760 | 0.412305 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.23695 | 0.173890 | 0.0869450 | − | 0.996213i | \(-0.472290\pi\) | ||||
0.0869450 | + | 0.996213i | \(0.472290\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.69774 | −0.321654 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.2519 | −0.439054 | −0.219527 | − | 0.975606i | \(-0.570451\pi\) | ||||
−0.219527 | + | 0.975606i | \(0.570451\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.8206 | 1.28477 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.6399 | 1.47254 | 0.736268 | − | 0.676690i | \(-0.236586\pi\) | ||||
0.736268 | + | 0.676690i | \(0.236586\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.41081 | −0.310097 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.2489 | −1.39064 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.1117 | −0.364956 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.36215 | 0.274353 | 0.137177 | − | 0.990547i | \(-0.456197\pi\) | ||||
0.137177 | + | 0.990547i | \(0.456197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.03027 | −0.0992067 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.76234 | −0.0902416 | −0.0451208 | − | 0.998982i | \(-0.514367\pi\) | ||||
−0.0451208 | + | 0.998982i | \(0.514367\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.0813 | −1.14484 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.7224 | −0.512536 | −0.256268 | − | 0.966606i | \(-0.582493\pi\) | ||||
−0.256268 | + | 0.966606i | \(0.582493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.0044 | −0.716563 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.6932 | 0.379979 | 0.189989 | − | 0.981786i | \(-0.439155\pi\) | ||||
0.189989 | + | 0.981786i | \(0.439155\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.4431 | 1.24792 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.0467 | −0.455496 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.83507 | −0.124230 | −0.0621151 | − | 0.998069i | \(-0.519785\pi\) | ||||
−0.0621151 | + | 0.998069i | \(0.519785\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.5211 | −0.372423 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4160 | −0.981163 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.90974 | −0.222663 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.3745 | 1.20188 | 0.600942 | − | 0.799292i | \(-0.294792\pi\) | ||||
0.600942 | + | 0.799292i | \(0.294792\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27.2419 | −0.875137 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.5783 | 1.43058 | 0.715292 | − | 0.698825i | \(-0.246294\pi\) | ||||
0.715292 | + | 0.698825i | \(0.246294\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.7664 | −0.408432 | −0.204216 | − | 0.978926i | \(-0.565464\pi\) | ||||
−0.204216 | + | 0.978926i | \(0.565464\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.8208 | −0.537595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.4992 | 0.558706 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.7641 | 0.502797 | 0.251399 | − | 0.967884i | \(-0.419109\pi\) | ||||
0.251399 | + | 0.967884i | \(0.419109\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.0071 | 1.08136 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.57162 | −0.0499241 | −0.0249620 | − | 0.999688i | \(-0.507946\pi\) | ||||
−0.0249620 | + | 0.999688i | \(0.507946\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.99441 | −0.221961 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.7367 | 0.720078 | 0.360039 | − | 0.932937i | \(-0.382763\pi\) | ||||
0.360039 | + | 0.932937i | \(0.382763\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25.9489 | 0.820987 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9800.2.a.cj.1.4 | 4 | ||
5.4 | even | 2 | 9800.2.a.ct.1.1 | 4 | |||
7.2 | even | 3 | 1400.2.q.m.1201.1 | yes | 8 | ||
7.4 | even | 3 | 1400.2.q.m.401.1 | yes | 8 | ||
7.6 | odd | 2 | 9800.2.a.cu.1.1 | 4 | |||
35.2 | odd | 12 | 1400.2.bh.j.249.7 | 16 | |||
35.4 | even | 6 | 1400.2.q.l.401.4 | ✓ | 8 | ||
35.9 | even | 6 | 1400.2.q.l.1201.4 | yes | 8 | ||
35.18 | odd | 12 | 1400.2.bh.j.849.7 | 16 | |||
35.23 | odd | 12 | 1400.2.bh.j.249.2 | 16 | |||
35.32 | odd | 12 | 1400.2.bh.j.849.2 | 16 | |||
35.34 | odd | 2 | 9800.2.a.ck.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.q.l.401.4 | ✓ | 8 | 35.4 | even | 6 | ||
1400.2.q.l.1201.4 | yes | 8 | 35.9 | even | 6 | ||
1400.2.q.m.401.1 | yes | 8 | 7.4 | even | 3 | ||
1400.2.q.m.1201.1 | yes | 8 | 7.2 | even | 3 | ||
1400.2.bh.j.249.2 | 16 | 35.23 | odd | 12 | |||
1400.2.bh.j.249.7 | 16 | 35.2 | odd | 12 | |||
1400.2.bh.j.849.2 | 16 | 35.32 | odd | 12 | |||
1400.2.bh.j.849.7 | 16 | 35.18 | odd | 12 | |||
9800.2.a.cj.1.4 | 4 | 1.1 | even | 1 | trivial | ||
9800.2.a.ck.1.4 | 4 | 35.34 | odd | 2 | |||
9800.2.a.ct.1.1 | 4 | 5.4 | even | 2 | |||
9800.2.a.cu.1.1 | 4 | 7.6 | odd | 2 |